On the equality condition in Hölder's and Minkowski's inequalities. (Summary).
On the equivalence of Hille's and Robinson's functional equations
On the existence and uniqueness of convex solutions of a functional equation in the indeterminate case
On the existence and uniqueness of integrable solutions of functional equations in Banach space.
On the existence and uniqueness of solutions of some partial differential functional equations
On the existence and uniqueness of the solution of a non-linear functional equation of r-th order
On the existence of a compactly supported -solution for two-dimensional two-scale dilation equations
Necessary and sufficient conditions for the existence of compactly supported -solutions for the two-dimensional two-scale dilation equations are given.
On the existence of a convex solution of the functional equation φ(x) = h(x,φ[f(x)])
On the existence of a Lipschitz solution of a functional equation
On the existence of continuous solutions of operator equations in Banach spaces
On the exponential function and Pólya's proof
On the extension of exponential polynomials
Exponential polynomials are the building bricks of spectral synthesis. In some cases it happens that exponential polynomials should be extended from subgroups to whole groups. To achieve this aim we prove an extension theorem for exponential polynomials which is based on a classical theorem on the extension of homomorphisms.
On the extension of integrable solutions of a functional equation of n-th order
On the formal first cocycle equation for iteration groups of type II
Let x be an indeterminate over ℂ. We investigate solutions αn : ℂ → ℂ, n ≥ 0, of the first cocycle equation in ℂ [[x]], the ring of formal power series over ℂ, where (F(s,x))s ∈ ℂ is an iteration group of type II, i.e. it is a solution of the translation equation of the form F(s,x) ≡ x + ck(s)xk mod xk+1, where k ≥ 2 and ck ≠ 0 is necessarily an additive function. It is easy to prove that the coefficient functions αn(s) of are polynomials in ck(s).It is possible to replace...
On the functional equation.
On the Functional Equation
On the functional equation defined by Lie's product formula
Let E be a real normed space and a complex Banach algebra with unit. We characterize the continuous solutions f: E → of the functional equation .
On The Functional Equation f = fg
On the functional equation f = fg.
On the Functional Equation f phi f = f